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Stability in probability of nonlinear stochastic systems with delay. (English. Russian original) Zbl 0843.93086
Math. Notes 57, No. 1, 103-106 (1995); translation from Mat. Zametki 57, No. 1, 142-146 (1995).
This paper considers a stochastic differential equation with a right hand side that has terms that are linear in delayed state, terms where delayed states are multiplied by Wiener processes, and terms that are nonlinear functions of the delayed state with available upper bounds in terms of the powers of the state. The Lyapunov method is used to derive a sufficient condition for the stability in probability of the null solution.

MSC:
93E15 Stochastic stability in control theory
93C10 Nonlinear systems in control theory
34K35 Control problems for functional-differential equations
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